Problem: $ 27^{-\frac{2}{3}}$
Explanation: $= \left(\dfrac{1}{27}\right)^{\frac{2}{3}}$ $= \left(\left(\dfrac{1}{27}\right)^{\frac{1}{3}}\right)^{2}$ To simplify $\left(\dfrac{1}{27}\right)^{\frac{1}{3}}$ , figure out what goes in the blank: $\left(? \right)^{3}=\dfrac{1}{27}$ To simplify $\left(\dfrac{1}{27}\right)^{\frac{1}{3}}$ , figure out what goes in the blank: $\left({\dfrac{1}{3}}\right)^{3}=\dfrac{1}{27}$ so $ \left(\dfrac{1}{27}\right)^{\frac{1}{3}}=\dfrac{1}{3}$ So $\left(\dfrac{1}{27}\right)^{\frac{2}{3}}=\left(\left(\dfrac{1}{27}\right)^{\frac{1}{3}}\right)^{2}=\left(\dfrac{1}{3}\right)^{2}$ $= \left(\dfrac{1}{3}\right)\cdot\left(\dfrac{1}{3}\right)$ $= \dfrac{1}{9}$